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Seismic Modeling, Migration and VelocityInversion
Full Waveform Inversion
Bee Bednar
Panorama Technologies, Inc.14811 St Marys Lane, Suite 150
Houston TX 77079
May 18, 2014
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 1 / 30
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Outline
1 Full Waveform InversionThe Basic Idea
2 Marmousi ExampleEstimating the Initial ModelFWI
MarmousiSEG AA′
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 2 / 30
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Full Waveform Inversion
Outline
1 Full Waveform InversionThe Basic Idea
2 Marmousi ExampleEstimating the Initial ModelFWI
MarmousiSEG AA′
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 3 / 30
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Full Waveform Inversion The Basic Idea
Full Waveform Inversion (FWI)
Velocity inversion is based on a very simple idea.Find that
Earth model M that best explains the recorded data D
Synthetic data U generated over M should match D as closely as
possible
Minimize an objective function ‖ D − U ‖ where ‖ − ‖ is theL1
normleast squares normleast squares norm of the phase difference
between D and Uleast squares norm of the envelope difference
between D and Uleast squares norm of the logarithmic difference
between D and U
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 4 / 30
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Full Waveform Inversion The Basic Idea
The Inversion Scheme
In the classical least squares case FWI is an iterative
scheme
Mn = Mn−1 − Rn−1 (D − U)
whereAt each iteration Rn−1
Is a very fancy imaging conditionProduces an incremental ∆MIs
almost always some form of reverse time migration
But it need not be
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 5 / 30
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Full Waveform Inversion The Basic Idea
Full Waveform Inversion
For a given modelFor each observed shot, synthesize data to
match the real acquisition
Use a full two-way modeling algorithmSave a trace at each model
node
Compute the difference between the shot and the real dataThese
data are called the residuals
Back propagated the residuals into the modelUse a full two-way
modeling algorithmSave a trace at each model node
Preform a shot-profile migration of the residualsThe shot is the
forward-propagated syntheticThe receiver traces are the
back-propagated residualsDivide the back by the forward propagated
traces
Normalize the image above by the velocity squaredAdd the
normalized image to the current modelRepeat the previous steps
until the norm of the model difference is small
FWI is really a iterative migration scheme
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 6 / 30
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Marmousi Example
Outline
1 Full Waveform InversionThe Basic Idea
2 Marmousi ExampleEstimating the Initial ModelFWI
MarmousiSEG AA′
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 7 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
(a) Gather Picks (b) Semblance Picks (c) NMO’d Gather
Typical Marmousi gather with picks, a semblance panel with
picks, and theNMO corrected gather.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 8 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
(a) Marmousi Time-RMS model (b) Marmousi Depth-Interval
model
Initial stacking velocity models in time-RMS (left) and
interval-depth (right).
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 9 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
First iteration Marmousi stacking velocity based Kirchhoff
migration.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 10 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
(a) Marmousi Time-RMS model (b) Marmousi Depth-Interval
model
Second Kirchhoff based MVA models in time-RMS (left) and
interval-depth(right).
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 11 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
Second iteration Marmousi Kirchhoff based MVA Kirchhoff
migration.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 12 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
(a) Marmousi Time-RMS model (b) Marmousi Depth-Interval
model
Second Kirchhoff based MVA models in time-RMS (left) and
interval-depth(right).
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 13 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
Third iteration Kirchhoff based MVA Kirchhoff migration.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 14 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
Fourth iteration Kirchhoff MVA based velocity model.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 15 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
Fourth iteration Kirchhoff MVA based Kirchhoff migration.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 16 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
Bottom horizon for constant velocity analysis.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 17 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
Fourth iteration Kirchhoff MVA based model with bottom horizon
4000meter/second velocity flood.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 18 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
Fourth iteration Kirchhoff MVA based model with bottom horizon
4000meter/second velocity flood migration.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 19 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
Fourth iteration Kirchhoff MVA based model with bottom horizon
5000meter/second velocity flood migration.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 20 / 30
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Marmousi Example Estimating the Initial Model
Marmousi MVA
The true Marmousi model.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 21 / 30
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Marmousi Example Estimating the Initial Model
Notes
Insufficient offsetMax of 2600 over 9000 km modelApproximately
1300 km velocity analysis basement
Recording time too short (3 seconds)Long delay wavelet
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 22 / 30
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Marmousi Example FWI
Marmousi FWI
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 23 / 30
Lavf54.29.104
marmousi-inversion-combo-aspect-2014-01-24-iter124.mp4Media File
(video/mp4)
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Marmousi Example FWI
Marmousi Inversion
True Marmousi model.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 24 / 30
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Marmousi Example FWI
Process Review
The true modelNine km by three km (depth)
The observed dataNine km offsetBroadband wavelet from .3 HZ to
50 HZ
Low frequency and long offsets are the key
Five second recording timeModel grid was 16m X 16m
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 25 / 30
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Marmousi Example FWI
The observed data
Marmousi Synthetic Data
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 26 / 30
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Marmousi Example FWI
The inversion process
We started with a MVA modelVirtually no reflectionsReasonably
accurate shallowFirst iteration essentially muted the first
breaksFirst iteration is exactly equivalent to migrating with our
initial model
Lailly: Migration is the first step in inversion
We calculated a new velocity model from residuals and a
synthetic shotWe shot a new synthetic data setWe imaged the
residualsWe repeated the exercise until model differences became
negligibleIn this case the model is as good as can be expected
This kind of inversion is theoretically valid for all Earth
Models.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 27 / 30
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Marmousi Example FWI
SEG AA′ FWI
We begin with a v(z) model and iterated for about 100
iterations.
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 28 / 30
Lavf54.29.104
segaap-inversion-2014-02-14.mp4Media File (video/mp4)
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Marmousi Example FWI
FWI Summary
Requires low frequenciesThe lower the better
Requires long offsetsThe longer the better
Generally gets the slow velocitiesMany iterations for fast
velocity anomalies
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 29 / 30
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Marmousi Example FWI
Questions?
Bee Bednar (Panorama Technologies) Seismic Modeling, Migration
and Velocity Inversion May 18, 2014 30 / 30
Main PartFull Waveform InversionThe Basic Idea
Marmousi ExampleEstimating the Initial ModelFWI